I’m a lecturer, and mature students dress in all different ways, as do younger students - jeans and trainers, dresses, skirts, dungarees, whatever. Practically speaking, some rooms in my place are freezing, others boiling, so you might need layers. You will also need a decent sized bag for carting stuff about - most of my students bring laptops or tablets, plus note pads, books, water etc. Kankens are popular, but lots of females have big slouchy handbags.
Staff tend to dress to suit their subject, so law lecturers are more likely to wear suits, whereas people like me in creative subjects are more casual. What I do find is that mature female students are more likely to “dress up” for things like giving presentations, often putting me to shame - I don’t know if that’s to help them feel more confident or if they have previously been expected to be smart in a work environment.
Staff in my work all wear lanyards with an ID card, which is often the only way you can tell they aren’t students.